Heat the oven to 425°F and line a large rimmed baking sheet with parchment paper.

Put the potatoes in a large pot and cover with cold water by 1 inch; add 1 teaspoon of the salt. Bring to a boil, then simmer for 15–20 minutes, until the potatoes are easily pierced with a fork.

While the potatoes cook, melt 1 tablespoon of the butter in a small skillet over low heat. Add the garlic and cook for 1 minute, stirring, until fragrant but not browned; add the remaining 3 tablespoons butter and stir until melted.

Drain the potatoes well and return them to the hot pot over low heat for 1–2 minutes, shaking the pot occasionally, until dry. Rice the potatoes into a large bowl, or mash until completely smooth.

Stir the garlic butter, warm cream, Parmesan, remaining 1/2 teaspoon salt, and pepper into the potatoes. Let the mixture cool for 5 minutes, then gently mix in the egg yolks until evenly combined.

Fit a piping bag with a 1/2-inch open-star tip and fill it with the potato mixture. Pipe 12 rosettes onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 15–20 minutes, until the ridges are golden and the center of a rosette reaches 160°F. Rest for 5 minutes before serving.